In the parallel structure, should I omit "become" if the subject is noun [closed]
Solution 1:
There is a history to parallelisms like this, in which the verb to be or some other verb is omitted. The omission itself was almost an announcement like a roll of drums: "this is a universal truth". This style of expression was called in ancient Greece αποφθεγμα (apophthegm - pronounced apofthem). The pre-socratic proponent of an early version of atomic theory, Demokritos, wrote (on another topic):
"The world (cosmos) a stage set life a chorus entry you came you saw you left" . We can't go quite that far in leaving out verbs. A couple of centuries later, the Alexandrian poet Callimachus, rebelling against traditional epic poetry, in favour of short, lighter so-called 'mini-epic' (epyllion - επυλλιον) declared, portentously:-
Μεγα βιβλιον μεγα κακον (Big book, big evil/trouble/bore - he probably meant all three at once).
What is the 'grammar' of this? In the Demokritos saying it's easy. We are left to assume the (unstated) verb is. The cosmos is a stage set. So you could say that there is a verb, and so the word string does constitute a sentence, but one with an ellipse. By the convention of apophthegms we are allowed not to bother with the copula.
But with Callimachus' declaration of rebellion, what is the verb here? You could say "is": a big book is a big bore. There are sayings like this in English, not least the those concerning big feet and those, conversely and more topically, concerning small hands. What we have here is the 'grammar' of juxtaposition, which we understand without putting it into words: big/small A implies/goes together with big/small B; or you could say show me big/small A and I'll show you big/small B; or that if (or where) you findbig/small A, then/there you will also find big/small B. There doesn't have to be a particular verb at all. Similarly with the ancient pithy apophthegm nothing too much (μηδεν αγαν / meeden agan). You can say that we are expected to think the verb do and so complete a grammatical imperative sentence, something like "Don't do anything to excess". In English, we say "moderation in all things". Is this a sentence fragment? If you like, you can call it that, but in that case you also have to say that there are sentence fragments with which there is nothing wrong.
Which brings me to your example:
The deeper the river, the greater the danger.
I should say that it is a proverb, like the ancient apophthegm, and that, like the apophthegm, it does not need a verb. Any 'proper' sentence is weaker than the pithy proverbial structure.
For any river, the danger increases in proportion to its depth.